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Proof step 18 from proof le-abs-numerator (previous step)

i < 0, 0 < i / j + i, 0 ≤ i ∧ 0 < j → i / j * j ≤ i ⊦ j = 0, j < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
0 < j, i < 0, 0 < i / j + i ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → (j ≤ i ↔ false); (as)%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ i < j → ¬ j < i; (s)% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)